On a

On a specialized website, you want to mix your own muesli. 200 g of muesli base costs 170 CZK. You want to add cornflakes in chocolate to the basics. 50g of this ingredient costs 13 CZK. How much do you pay for a 150g mixture when the weight of both components is the same?

Correct answer:

x =  83.25 Kc

Step-by-step explanation:

$$\begin{gathered} m_1=200\text{g} \\ {c}_1=170\text{kc} \\ {m}_2=50\text{g} \\ {c}_2=13\text{Kc} \\ m=150/2=75\text{g} \\ {x}_1=\frac{m}{m_1}\cdot c_1=\frac{75}{200}\cdot 170=\frac{75\cdot 170}{200}=\frac{12750}{200}=\frac{255}{4}=63.75\text{Kc} \\ {x}_2=\frac{m}{m_2}\cdot c_2=\frac{75}{50}\cdot 13=\frac{75\cdot 13}{50}=\frac{975}{50}=\frac{39}{2}=19.5\text{Kc} \\ x=x_1+x_2=\frac{255}{4}+\frac{39}{2}=\frac{255}{4}+\frac{78}{4}=\frac{255+78}{4}=\frac{333}{4}=\frac{333}{4}\text{Kc}=83.25\text{Kc} \end{gathered}$$

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